Building on statistical foundations laid by Neyman [1923] a century ago, a growing literature focuses on problems of causal inference that arise in the context of randomized experiments where the target of inference is the average treatment effect in a finite population and random assignment determines which subjects are allocated to one of the experimental conditions. In this framework, variances of average treatment effect estimators remain unidentified because they depend on the covariance between treated and untreated potential outcomes, which are never jointly observed. Aronow et al. [2014] provide an estimator for the variance of the difference-in-means estimator that is asymptotically sharp. In practice, researchers often use some form of covariate adjustment, such as linear regression when estimating the average treatment effect. Here we extend the Aronow et al. [2014] result, providing asymptotically sharp variance bounds for general regression adjustment. We apply these results to linear regression adjustment and show benefits both in a simulation as well as an empirical application.

翻译：基于Neyman [1923] 在一个世纪前奠定的统计学基础，越来越多的文献关注随机化实验背景下出现的因果推断问题，其中推断目标为有限总体中的平均处理效应，而随机分配决定了哪些受试者被分配到实验条件之一。在此框架下，平均处理效应估计量的方差仍无法识别，因为它们取决于处理组与未处理组潜在结果之间的协方差，而这些结果从未被同时观测到。Aronow 等人 [2014] 提出了一种用于差分均值估计量方差的估计器，该估计器是渐近最优的。在实践中，研究者通常使用某种形式的协变量调整，例如在估计平均处理效应时采用线性回归。本文扩展了 Aronow 等人 [2014] 的结果，为一般回归调整提供了渐近最优的方差界。我们将这些结果应用于线性回归调整，并通过模拟和实证应用展示了其优势。